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Trefftz Methods and Taylor Series

Abstract : The paper discusses Trefftz discretization techniques with a focus on their coupling with shape functions computed by the method of Taylor series. The paper highlights are, on one hand the control of ill-conditioning and the solving of large scale problems, on the other hand the applications to non-linear Partial Differential Equations. Indeed, despite excellent convergence properties, the practical use of Trefftz methods remains very limited because of their difficulty in treating nonlinearities and large systems.
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https://hal.univ-lorraine.fr/hal-03251176
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Submitted on : Sunday, June 6, 2021 - 4:16:36 PM
Last modification on : Wednesday, November 3, 2021 - 9:00:43 AM

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Jie Yang, Michel Potier-Ferry, Koffi Akpama, Heng Hu, Yao Koutsawa, et al.. Trefftz Methods and Taylor Series. Archives of Computational Methods in Engineering, Springer Verlag, 2020, 27 (3), pp.673-690. ⟨10.1007/s11831-019-09330-2⟩. ⟨hal-03251176⟩

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